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The planar restricted three-body problem when both primaries are triaxial rigid bodies: Equilibrium points and periodic orbits

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Abstract

The restricted three-body problem when the primaries are triaxial rigid bodies is considered and its basic dynamical features are studied. In particular, the equilibrium points are identified as well as their stability is determined in the special case when the Euler angles of rotational motion are accordingly \(\theta_{i} = \psi_{i} = \pi/2\) and \(\varphi_{i} = \pi/2\), \(i = 1, 2\). It is found that three unstable collinear equilibrium points exist and two triangular such points which may be stable. Special attention has also been paid to the study of simple symmetric periodic orbits and 31 families consisting of such orbits have been determined. It has been found that only one of these families consists entirely of unstable members while the remaining families contain stable parts indicating that other families bifurcate from them. Finally, using the grid-search technique a global solution in the space of initial conditions is obtained which comprises simple and of higher multiplicities symmetric periodic orbits as well as escape and collision orbits.

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Acknowledgements

The authors would like to thank the unknown referee and the editor for thoughtful comments, which led to the improvement of the present paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt

    S. M. Elshaboury

  2. Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt

    Elbaz I. Abouelmagd

  3. Department of Electrical and Computer Engineering, University of Patras, 26500, Patras, Greece

    V. S. Kalantonis & E. A. Perdios

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  1. S. M. Elshaboury
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  2. Elbaz I. Abouelmagd
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  3. V. S. Kalantonis
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  4. E. A. Perdios
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Correspondence to Elbaz I. Abouelmagd.

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Elshaboury, S.M., Abouelmagd, E.I., Kalantonis, V.S. et al. The planar restricted three-body problem when both primaries are triaxial rigid bodies: Equilibrium points and periodic orbits. Astrophys Space Sci 361, 315 (2016). https://doi.org/10.1007/s10509-016-2894-x

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